McCarney's lawyers are now considering whether to go to Strasbourg in an effort to have his conviction for the murder of 15-month-old Millie Martin overturned.

Millie died in December 2009 after being admitted to hospital in Enniskillen, Co Fermanagh, with serious injuries.

She had sustained multiple fractured ribs, heavy bruising and a burnt finger.

McCarney (35), formerly of Trillick, Co Tyrone, had started a relationship with Millie's mother Rachael, and moved into the family home in Enniskillen months before her death.

In December 2012 a jury reached a verdict that he had murdered the child.

He was also convicted of sexual assault and causing grievous bodily harm to her.

Rachael Martin was acquitted at trial of allowing her daughter's death and cruelty through wilful neglect.

Last month McCarney failed in a bid to have his convictions overturned amid claims he had not received a fair trial.

Judges at the Court of Appeal in Belfast rejected legal arguments based around interpretations of the Domestic Violence, Crime and Victims Act 2004 which featured in the case.

Prison guards escorted McCarney back into court yesterday for a planned challenge to the minimum 25-year tariff imposed on him. But his barrister, Eilis McDerrmott QC, said: "Having taken instructions this morning I can tell the court that Mr McCarney doesn't wish to proceed with his appeal against sentence."

She then requested leave to take the case to the Supreme Court as part of continuing efforts to overturn the convictions.

The application was based on continued claims that the trial process had been unfair. But denying permission, Lord Justice Higgins, sitting with Lord Justice Coghlin and Mr Justice Horner, ruled that no point of law of general public importance had been established.

It is understood that McCarney's legal team are now considering whether to ask the European Court of Human Rights in Strasbourg to examine the case.

Solicitor Conor Heaney explained why the bid to have his client's prison term reduced was abandoned.

He said outside court: "Mr McCarney has decided not to pursue any application to appeal against his sentence as he considers that would dilute his concerted efforts to have his wrongful conviction in respect of the death of Millie Martin overturned."